Model Diagnostics

We created Bayesian Logistic Regression models using the open-source rstanarm package for the statistical programming language R.

Our model analyzes the relationship between the PEDIS-system, a clinical classification to describe characteristics of Diabetic Foot Ulcers, and amputation, which results from such ulcers as a severe complication.

We used two distinct amputation definitions:

  1. Any Amputation excluding the lesser toes (This definition entails minor and major amputation, whereas major amputations are on the level of the lower limb or even more proximal, e.g., knee or thigh).

Furthermore, we scrutinized the impact of an informed prior compared to a non-informed one.

As a result, we created four distinct model.

  1. Non-informed with any-amputation
  2. Non-informed with major-amputation
  3. Informed with any-amputation
  4. Informed with major-amputation

Non-informed Models

Any Major

model1 <- readRDS("models/any-amputation-non-informed.RDS") %>% pluck(4)
## Warning: namespace 'pedis' is not available and has been replaced
## by .GlobalEnv when processing object ''
color_scheme_set("viridis")

# Effect size
summary(model1) %>% 
  as.data.frame() %>% 
  as_tibble(rownames = "Predictors") %>% 
  select(Predictors, n_eff) %>% 
  slice(1:8) %>% 
  kable() %>% 
  kableExtra::kable_styling(bootstrap_options = "striped", full_width = F)
Predictors n_eff
(Intercept) 26516
p 24728
e_ordinal_5 25087
d 26378
i 28326
s 32397
alter_bei_aufnahme 28275
gender 31458 
# MCMC trace
mcmc_trace(model1)

# Scatterplots of MCMC draws
mcmc_pairs(x = model1, pars = c("p", "e_ordinal_5", "d", "i", "s"))

# Posterior predictive check
pp_check(model1)

Major Amputation

model1 <- readRDS("models/any-amputation-non-informed.RDS") %>% pluck(4)
## Warning: namespace 'pedis' is not available and has been replaced
## by .GlobalEnv when processing object ''
color_scheme_set("viridis")

# Effect size
summary(model1) %>% 
  as.data.frame() %>% 
  as_tibble(rownames = "Predictors") %>% 
  select(Predictors, n_eff) %>% 
  slice(1:8) %>% 
  kable() %>% 
  kableExtra::kable_styling(bootstrap_options = "striped", full_width = F)
Predictors n_eff
(Intercept) 26516
p 24728
e_ordinal_5 25087
d 26378
i 28326
s 32397
alter_bei_aufnahme 28275
gender 31458 
# MCMC trace
mcmc_trace(model1)

# Scatterplots of MCMC draws
mcmc_pairs(x = model1, pars = c("p", "e_ordinal_5", "d", "i", "s"))

# Posterior predictive check
pp_check(model1)

Informed Models

Any Amputation

model1 <- readRDS("models/any-amputation-informed.RDS") %>% pluck(4)
## Warning: namespace 'pedis' is not available and has been replaced
## by .GlobalEnv when processing object ''
color_scheme_set("viridis")

# Effect size
summary(model1) %>% 
  as.data.frame() %>% 
  as_tibble(rownames = "Predictors") %>% 
  select(Predictors, n_eff) %>% 
  slice(1:8) %>% 
  kable() %>% 
  kableExtra::kable_styling(bootstrap_options = "striped", full_width = F)
Predictors n_eff
(Intercept) 25945
p 29933
e_ordinal_5 23116
d 27226
i 26024
s 33476
alter_bei_aufnahme 28278
gender 30840 
# MCMC trace
mcmc_trace(model1)

# Scatterplots of MCMC draws
mcmc_pairs(x = model1, pars = c("p", "e_ordinal_5", "d", "i", "s"))

# Posterior predictive check
pp_check(model1)

Major Amputation

model1 <- readRDS("models/major-amputation-informed.RDS") %>% pluck(4)
## Warning: namespace 'pedis' is not available and has been replaced
## by .GlobalEnv when processing object ''
color_scheme_set("viridis")

# Effect size
summary(model1) %>% 
  as.data.frame() %>% 
  as_tibble(rownames = "Predictors") %>% 
  select(Predictors, n_eff) %>% 
  slice(1:8) %>% 
  kable() %>% 
  kableExtra::kable_styling(bootstrap_options = "striped", full_width = F)
Predictors n_eff
(Intercept) 18853
p 28542
e_ordinal_5 17698
d 24427
i 28594
s 31812
alter_bei_aufnahme 29640
gender 31760 
# MCMC trace
mcmc_trace(model1)

# Scatterplots of MCMC draws
mcmc_pairs(x = model1, pars = c("p", "e_ordinal_5", "d", "i", "s"))

# Posterior predictive check
pp_check(model1)